ps4solutions - 14.03 Fall 2000 Problem Set 4 Solutions 1....

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 14.03 Fall 2000 Problem Set 4 Solutions 1. Nicholson 8.5 a. EU = 0.75ln(10000) + 0.25ln(9000) » 9.184 b. By purchasing full insurance at a premium of 250, Ms. Fogg’s wealth in each state becomes 9750. Hence her expected utility is ln(9750) » 9.185, which is greater than her expected utility if she does not buy insurance. c. The maximum amount that Ms. Fogg is willing to pay for full insurance is P s.t. ln(10000 – P ) = 0.75ln(10000) + 0.25ln(9000) By the properties of logs, ln(10000 – P ) = ln ( 10000 0.75 9000 0.25 ) P = 10000 - ( 10000 0.75 9000 0.25 )» 259.96 2. Part 1: Both of the risky choices (B and D) have higher expected values than the certain choices (A and C). If Bill were risk neutral or risk loving, he would prefer B to A and D to C. The fact that he is indifferent between them implies that he is risk averse. Part 2: The expected utility of F is EU ( F ) = .25 u (400) + .25 u (900) + .25 u (800) + .25 u (1500) EU ( F ) = .5(.5 u (400) + .5 u (900)) + .5(.5 u (800) + .5 u (1500)) EU ( F ) = .5 EU ( D ) + .5 EU ( B ) = .5 EU ( C ) + .5 EU ( A ) Then note that a 50/50 gamble over C and A has expected value $750. Since Bill is risk averse he will prefer $750 with certainty to this gamble. Hence he prefers E to F. 3. If choices are consistent with expected utility maximization, then there exists some utility function u (.) such that the lottery that gives wealth ( w 1 ,..., w n ) with probabilities ( p 1 ,..., p n ) is preferred to the lottery ( w 1 ',..., w n '), ( p 1 ',..., p n ') iff n n i = 1 p i u ( w i ) > i = 1 p i ' u ( w i ') . Thus A preferred to B implies that u (1m)>.1 u (5m)+.89 u (1m)+.01 u (0), or .11 u (1m)>.1 u (5m)+.01 u (0). And C preferred to D implies that .1 u (5m)+.9 u (0)>.11 u (1)+.89 u (0), or .1 u (5m)+.01 u (0)>.11 u (1m), which is a contradiction. Hence choosing A over B and C over D is inconsistent with expected utility maximization. U ( W ) = 100 W 0.9 4. U '( W ) = 90 W - 0.1 U ''( W ) = - 9 W - 1.1 9 W - 0.1 1 a) rr ( W ) = 90 W - 0.1 = 10 b) willingness to pay for full insurance is WTP such that U (1 - WTP ) = 0.9 U (1) + 0.1 U (0.9) 100(1 - WTP ) 0.9 = 0.9(100)(1) 0.9 + 0.1(100)(0.9) 0.9 1 WTP = 1 - (0.9 + 0.1(0.9) 0.9 ) 0.9 = 0.01004687 or about $10.05....
View Full Document

Page1 / 5

ps4solutions - 14.03 Fall 2000 Problem Set 4 Solutions 1....

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online